2000/08/03 by N S Skantzos, N. S. Skantzos, A C C Coolen +1 · 1 citation
Computer Science · Engineering · Neuroscience · Physics and Astronomy · #Advanced Memory and Neural Computing #Neural Networks and Applications #Neural dynamics and brain function #cond-mat.dis-nn
paper · pdf · doi:10.1088/0305-4470/34/5/301
published as J. Phys. A, 34 (2001) 929 · 16 pages, 15 postscript figures, Latex
arxiv created 2000/08/03 · openalex publication_date 2001/01/25 · arxiv updated 2009/11/30 · openalex created_date 2021/02/01 · openalex updated_date 2026/07/30
We extend a recently introduced class of exactly solvable models for recurrent neural networks with competition between one-dimensional nearest-neighbour and infinite-range information processing. We increase the potential for further frustration and competition in these models, as well as their biological relevance, by adding next-nearest-neighbour couplings, and we allow for modulation of the attractors so that we can interpolate continuously between situations with different numbers of stored patterns. Our models are solved by combining mean-field and random-field techniques. They exhibit increasingly complex phase diagrams with novel phases, separated by multiple first- and second-order transitions (dynamical and thermodynamic ones), and, upon modulating the attractor strengths, non-trivial scenarios of phase diagram deformation. Our predictions are in excellent agreement with numerical simulations.